/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.15104536]

Formerly >>15085518

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
images.google.com
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
annas-archive.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

Tips for asking questions here:
>attach an image (animal images are ideal, you can grab them from >>>/an/. Alternatively use anime from safebooru.donmai.us)
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.15104563]

Unanswered questions:

Maths questions:
>>15086077 [No.]
>>15087945
>>15088450
>>15089929
>>15091980 [I don't think there was a formal definition.]
>>15092122 [He clearly miscopied the question]
>>15095878
>>15097597
>>15101369
>>15101757

Physics questions:
>>15090792
>>15098395

Chemistry questions:
>>15100262

Maid questions (yes, there are questions in the posts):
>>15085630
>>15087981
>>15093088

Biology questions:
>>15087401
>>15088861
>>15094697
>>15100513

/g/ questions:
>>15088880
>>15094429

Stupid questions:
>>15087158
>>15087396
>>15090702
>>15094252
>>15094286
>>15095229
>>15095751
>>15097045
>>15100231
>>15100635
>>15102121
>>15103613

[Anonymous No.15104660]

>>15104563
>Maid questions
This made me giggle

>>15103613
Had a similar experience with Griffiths, i would recommend 'An Introduction to Quantum Physics' by A.P. French and Edwin F. Taylor

[Anonymous No.15104931]

>>15104536
Let U be the subspace of R_4 defined by the span of vectors [math]\begin{pmatrix}
-1,1,1, 0
\end{pmatrix}, \begin{pmatrix}
0,1,0,1
\end{pmatrix}[/math]. Find the matrix that represents the projection on U.

Alright so my result is [math]\begin{pmatrix}
2/5 &-1/5 &-2/5 &1/5\\
-1/5& 3/5 &1/5 &2/5 \\
-2/5&1/5 &2/5 &-1/5 \\
1/5& 2/5 &-1/5& 3/5 \\
\end{pmatrix}[/math]

first of all I want to know if what I did is right:
1. Gram Schmidt algorithm to get an orthonormal basis from the starting basis
2. Now I can apply the projection formula and with one full page of calculations i get to a matrix with 4 rows and 1 column where each row is in the form of eg for the first row: (2/5)x1-(1/5)x2-(2/5)x3+(1/5)x4
i conclude that this would be the same as having a 4x4 matrix (see matrix posted above) multiplied by a 4x1 vector (x1, x2, x3, x4), therefore L=Av where L is the projection endomorphism and A is the matrix I was looking for from the beginning.

Now, im fairly sure that this whole thing is right, maybe i did some calculations error but the idea behind it should be correct. The problem is that my teacher expects me to solve this in about 10 minutes and it took me about 45 minutes and i didnt even do all the calculations by hand, so i was thinking that there is some kind of shortcut that i didnt see to find this matrix

[Anonymous No.15104971]

>>15104931
>Now I can apply the projection formula
Do you mean the [math]A(A^TA)^{-1}A[/math] one? That doesn't need an orthonormal basis to work. You can just stick in the starting basis and you'll get the same matrix.

[Anonymous No.15105003]

>>15104971
Yes sorry I forgot to add ORTHOGONAL projection, so the orthogonal projection of a vector v on a subspace H, where b1...bn are the vectors of an orthonormal basis of H, the formula is:
[math]\pi_H(v)=<v,b_1>b_1+...+<v,b_n>b_n[/math]

i dont know about the thing you just posted, or maybe i dont recognize it right now, could you elaborate?

[Anonymous No.15105008]

>>15105003
also i really dont know about different notations but my teacher uses <.,.> to mean the standard scalar product (dot product in american literature i think)

[Anonymous No.15105062]

>>15105003
There is a formula for the matrix that projects a vector onto a subspace. If your subspace is spanned by a set of vectors, you use those as the columns of a matrix A, and then [math]A(A^TA}^{-1}A^T[/math] (I forgot a T the first time) is your projection matrix

it's still a bit of a pain in the ass to do by hand, but I think it's reasonable to expect students to do on an exam. I'm pretty sure I had to

[Anonymous No.15105118]

sup guys
I'm having some troubles understanding the direction of the torque in the example 1 in picrel

So, basically I drew a gyroscope experiment I saw on a lecture
the gyroscope is spinning and then a force is applied on one edge of the gyroscope

the torque I drew in red is correct but why is it so? shouldn't it be pointed towards the opposite direction?

for finding the direction of the torque I'm making the cross product between the force/weightforce I apply and the angular momentum (see example 2)

I mean, it makes sense that it spins the way it spins but i can't figure out why..
in order to make sense there should be a force pointing upwards, but what's that? is there even such a force? idk...

[Anonymous No.15105395]

I am given a circle C1 with origin O and radius R1. Given any point P1 on it, I need to find another point P2 "directly after it" (idk the right math term) which lies on another, larger and encapsulating circle C2, and I am given S = R2 - R1. Note that when P1 is on 0/90/180/270 degrees, the solution is trivial: just add S to P1x or P1y. For other points this will not work, as the line connecting the P2 and the origin does not pass through P1.

i hope that pic related is helpful

[Anonymous No.15105408]

>>15105395
>Note that when P1 is on 0/90/180/270 degrees, the solution is trivial: just add S to P1x or P1y.
or substract lmao; but you get it

[Anonymous No.15105472]

>>15089929
you need to sample at a rate of at least [math]2f[/math] to faithfully (kinda) capture a signal, where [math]f[/math] is the highest frequency contained in the signal. to capture a 1kHz sine wave, you need to sample at at least 2kHz. a square wave has infinitely high frequency components, so you can technically never truly capture a square wave, you can only be more and more reasonably certain its a square wave the higher you sample.
technically, you can never actually represent a continuous signal with discrete sampling. lets say you sample the peaks and troughs of a 1kHz sine wave (so youd be sampling at 2kHz). you could conclude that the signal is a 1kHz sine wave, but a sine wave of 2.5kHz would produce the exact same samples. these are called aliases, and the higher you sample, the farther out the aliases are; if you sample the 1kHz sine wave at 10kHz, the nearest alias is at 100kHz, i think. if youve ever seen video footage of something spinning really fast and noticed that the video made it look like it was spinning slowly, thats an example of aliasing.
https://en.wikipedia.org/wiki/Aliasing
https://en.wikipedia.org/wiki/Nyquist_frequency
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

[Anonymous No.15105494]

this is a really out there question and more a shower thought. Is there an evolutionary reason for fetishes? As a basic example, I know there are "legs" men who get really turned on by long legs. But, if every man had that then wouldn't we selectively evolve into leg abominations? I'm imagining something like birds where their tail feathers are so long it hinders them. Would a naturally evolved random distribution of fetishes prevent things like that?

[Anonymous No.15105888]

>>15105003
>[math]\pi_H(v)=<v,b_1>b_1+...+<v,b_n>b_n[/math]
Why are you writing the formula like that instead of [math]b_1 b_1^T + \ldots b_n b_n ^T[/math]? Also why did it take you a full page to calculate this?

[Anonymous No.15105908]

Supposebly, multiverse theory is widely accepted. If it is true, how does anything exist? Infinite infinities mean that there are an infinite amount of null sets of possibilities- universes made out of material that destroys time, or aliens that invent a bomb that can destroy everything. If there are infinite possible alternates, then anything is possible, which should mean that everything should be happening at the same time, but it doesnt. Why?

[Anonymous No.15105946]

Can you compress air using an air tight container with a large weight on it? Like say a non chemical way to compress them into tanks? (theoretically)

Also probably better suited for outdoors boards as its semi survivalist: has anyone ever invented a heat furnace under a house connected to pipes that go around the house with the furnace heating the water as a form of both supply hot water to taps and heating the house? I imagine you'd need a lot of heat to heat a lot of hot water and have it set up so the kinetic energy from the water is enough to allow the water to easily move up the house through the pipes.

[Anonymous No.15105955]

>>15104536
Why do all esoteric nerds like Touhou?

[Anonymous No.15105958]

>>15105494
Its probably person to person. Boobs generally for raising children. Legs often for strength to do work. Same with ass. Hips for birthing children. A lot of kinks are for strength, ie having an alpha male not a beta. But it can vary person to person.

[Anonymous No.15105990]

>>15105946
what do you think a piston is

[Anonymous No.15106003]

Why do I feel better when slightly hungry?

[Anonymous No.15106053]

>>15105888
I wrote the general formula to get the orthogonal projection of a vector on a subspace given an orthonormal basis of the subspace, but yes it's essentially the same thing as you posted I guess if we're not working with any specific vector but just want to know the general projection matrix.

>why did it take you a full page to calculate this
I mean do it yourself from the Grahm Schmidt algorithm to the end and you'll see that it takes quite a bit of space, easy algebra but lengthy process

[Anonymous No.15106055]

>>15106003
because its based

[Anonymous No.15106070]

>>15105908
Not how infinity works.
For all we know, there could be an infinite amount of universes, but the only difference between each of them is the Swahili word for "four"

[Anonymous No.15106120]

is the sylvester theorem usually covered in a typical first year linear algebra for engineering course?

[Anonymous No.15106130]

>>15105908
> multiverse theory is widely accepted
Nope. There is no proof it's true, but there is no scientific evidence it's false either.

[Anonymous No.15106147]

[math]f(x)=\frac{\sqrt{lnx}}{e^x}[/math]
I need to find a function in the form of [math]g(x)= \frac{1}{x^\alpha}[/math] such that i can say that f(x) <= g(x) for x -> +infinity.

my book says that the result is alpha=2, but im not sure how it got that result.

[Anonymous No.15106156]

>>15106147
not sure what happened with the latex but its still understandable i guess

[Anonymous No.15106183]

>>15105395
too hard?

[Anonymous No.15106189]

Let [math]G[/math] be a locally compact group. A conjugation invariant measure on [math]G[/math] is a positive Radon measure [math]\theta[/math] that satisfies [math]\theta(gAg^{-1}) = \theta(A)[/math] for all [math]g\in G[/math] and Borel [math]A \subset G[/math].

1. What are some reasonable assumptions on [math]G[/math] that imply the existence of such a measure? (For example, if [math]G[/math] is unimodular then the Haar measure serves.)
2. Must any such measure be a Haar measure? If not, can we still say that such a measure is unique up to scalars?

[Anonymous No.15106318]

>>15106189
>Must any such measure be a Haar measure? If not, can we still say that such a measure is unique up to scalars?
Nope. Consider G abelian, for example.
>What are some reasonable assumptions on G that imply the existence of such a measure?
Maybe if the inner automorphism group admits such a measure you can extend it to G.

[Anonymous No.15106334]

Why is paracetamol used for temperatures and not ibuprofen? Is it the metabolite am404?

[Anonymous No.15106533]

>>15105990
they just put those in engines to make them look cool

[Anonymous No.15106557]

>>15106147
Are you sure that's not the only typo since in the limit f(x) tends to zero?

[Anonymous No.15106588]

Let V be vector space containing the subspaces [math]U_{i} \subseteq W_{i}\subseteq V[/math] for [math]i \in I[/math].

Show that [math]\oplus_{i \in I}\, U_{i} = V[/math] implies [math]W_{i} = U_{i}[/math] for all [math]i \in I[/math].

This question confuses me, /sqt/. Couldn't I choose [math]W_{i} = V[/math] for all [math]i \in I[/math] as a counterexample? Even if you declared the [math]W_{i}[/math] subspaces to be pairwaise distinct, the implication would be wrong. What am I missing?

[Anonymous No.15106647]

So one of my homework problems is this. There is a star with mass = 10 solar masses. The distances with the log of the density (function of distance) divided by the core density is given in the table of pic related. Here the distance is denoted as r / R where R is the total radius of the star which is 4 times the radius of the sun.

Now I'm supposed to use numerical integration to find the core density, but I'm not entirely sure how to go about it. Any help here?

I've already tried using Runge Kutta 4 by turning the mass equation M = 4/3 * pi * r^3 * rho into dM/dr = 4 * pi * r^2 * rho but then you run into not knowing the core density so you can't compute the mass, which you need for finding the core density. I guess I'm missing something here but IDK how you could solve this knowing that there's practically 3 unknown variables in this equation.

Thanks in advance homies

[Anonymous No.15107200]

>>15105990
I feel like it's different. Pistons explode at different times so when one explodes up it's pushing rhe other down cause they rotate... The crank shaft? So they're using the energy of separate ones. Anyway. Wondering if anyone has ever compressed oxygen into tanks in that way in reality. It's kindve hard to Google and get a result on. I don't know why I don't know what value compressed oxygen in an odd grid setting would provide unless it were like in a bomb shelter post nuclear war

[Anonymous No.15107317]

>>15106557
yes i am, for example f(x) <= 1/x^2 definitely (and with definitely my teacher means "a property that holds from any point up to infinity", for example x^2 is definitely >= (5+lnx), in particular from the point 2.4...

[Anonymous No.15107453]

>>15107200
there are piston powered air compressors, the discharge of the last stage is piped into holding tanks at whatever the discharge psi is set to. It's exactly what youre describing but manually. Compressed pure o2 would be incredibly valuable in a post nuke setting, but compressed air? eh. just for breathing? its relatively simple to filter contamination from air

[Anonymous No.15107463]

>>15106070
there are also infinite odds numbers, sure, but that isnt what is being proposed. the idea is infinite permutations of the initial conditions of reality.

[Anonymous No.15107482]

>>15107463
Yes... which does not imply the possibility of "material that destroys time".

[Anonymous No.15107543]

>>15106647
Divide the star into spherical layers as suggested by the first column. Write an equation for the mass of each shell in terms of core density. Basically, you'll have one equation for each row in your table. Now sum those equations and set that sum equal to 10 solar masses. Solve for your core density.

This is probably most easily done in a spreadsheet.

[Anonymous No.15107567]

>>15105395
>I need to find another point P2 "directly after it" (idk the right math term)
You'd better find the right term or offer a better description because any solution is totally dependent on understanding this. The remainder of your statement suggests that the origin, P1, and P2 both are and are not colinear.

[Anonymous No.15107778]

>>15107453
Ok thanks. What is 02 useful for

[Anonymous No.15108092]

https://github.com/mkirchner/linked-list-good-taste
The important quote is:
>I don't want you to understand why it doesn't have the if statement. But I want you to understand that sometimes you can see a problem in a different way and rewrite it so that a special case goes away and becomes the normal case, and that's good code.
Does math have something equivalent to this?

[Anonymous No.15108183]

Assuming suicide before one would likely die from natural causes was required and it was to occur when there is evidence of consistent decline in physical and mental ability at what is the youngest age that such a decline in physical and mental ability would be universally present in humans?

[Anonymous No.15108228]

>>15104536
Isn't every base technically base 10? For instance 2 in base 2 is 10, 3 in base 3 is 10 etc

[Anonymous No.15108248]

>>15108228
It's basically how many symbols you pass through
to get to ten. In binary: 0,1...then 10. How about
in hexadecimal? 0,1,2,...,9,A,B,C,D,E,F...then 10.

[Anonymous No.15108280]

>>15107567
O, P1 and P2 are not collinear.

Let's try like this:
Imagine straight lines, one vertical and one horizontal, going through P1. All I need to find is where these lines intersect C2.

[Anonymous No.15108375]

are there machine learning models that can predict the transformation of a small cutout from a larger image, with the inputs being both the cutout and the original image and the outputs a transformation matrix or xy, rotation etc. (or a paper describing the model)

[Anonymous No.15108404]

>>15104563
>maid questions
>mfw
I solved the character set problem by just using ISO-8859-1. Instead of specifying my characters I just count from 0 to 255 and cast it to character using that character set.

I planned to release Kurumi MaidCard a few days ago, but then I found bugs. I hope to repair them all today and release it. It goes kind of slow sometimes because the maid is having problems.

I still would like it if someone can tell me a book that explains how arithmetic can be formed with logical operators and/or successor function. Grzegorczyk Hierarchy was what Wikipedia said but I didn't have luck finding materials.

Thank you whoever told me to get the Geometric Magic Squares book. I like that it has a very high amount of drawings and is printed on nice paper like Wolfy's books are.

Thank you /sci/entists for reading my post.

[Anonymous No.15108636]

God I fucking hate applied "mathematics" book. Can someone recommend me a REAL statistics book please?

[Anonymous No.15108650]

>>15108636
It's a very simple theorem to prove tbqhwy. You should be able to do it (unironically).

[Anonymous No.15108689]

>>15108650
Oh yeah? Now prove this.

[Anonymous No.15108776]

>>15108280
That's much clearer. Here you go.

[Anonymous No.15108861]

>>15108689
nta

[Anonymous No.15108955]

>>15106003
Pre-initiation of fasting processes

[Anonymous No.15108982]

>>15108861
Literally the first line you used something not discussed in the book (barring a small endnote), so fail.

[Anonymous No.15108989]

existence is pain

[Anonymous No.15109036]

>>15108982
There is a reason your book skips the proof you know

[Anonymous No.15109041]

How bad is it to have just a single failed class due to low attendance?

[Anonymous No.15109152]

let [math]V[/math] be a 2 dimensional inner product space over [math]\mathbb{R}[/math]. I'm trying to prove there exist no three unit vectors [math]v_1, v_2 ,v_3 \in V[/math] for which [math]|| v_1 - v_2|| = ||v_2 - v_3|| = ||v_1 - v_3|| = 1[/math]. I can show that if [math]span(v_1, v_2, v_3)[/math] is 1 dimensional then a contradiction arises, but other than that, I'm stuck. any help is appreciated

[Anonymous No.15109161]

>>15109152
>it's an "anon is trying to prove equilateral triangles don't exist" episode

[Anonymous No.15109184]

>>15109152
>>15109161
Ooh, *unit* vectors.
Gee anon, just write down "any equilateral triangle inscribed on the unit circle has side [math]\sqrt{3}[/math]."

[Anonymous No.15109210]

>>15109184
lol yeah, unit vectors.
>any equilateral triangle inscribed on the unit circle has side [math]\sqrt{3}[/math]
does this hold for any inner product one can put on a 2 dimensional real space tho? and if so.. why?

[Anonymous No.15109232]

>>15109210
>does this hold for any inner product one can put on a 2 dimensional real space tho?
You know that they're all isometric right?

[Anonymous No.15109282]

>>15109232
not sure what you mean by that. I know only the basic stuff: inner product axioms, pythagorean theorem, triangle inequality, cauchy schwarz inequality.. that's all I've been taught so far

[Anonymous No.15109487]

>>15109041
depends, but even worse case its not that bad. you probably have way worse things to worry about :)

[Anonymous No.15109690]

how does semilogx work? for example i want to plot y=x and make the X-axis logarithmic. My understanding is I need to plot y=10^x and every value of x will be a power of 10. That works well except it gives non-sensical results when powers are involved. For example y=x^2. How would I need to change it to get the semilogx behavior? y=10^x^2 doesn't work. I thought maybe y=x^n should get converted to y=n10^x and that is close but still wrong.

[Anonymous No.15109718]

>>15109690
>make the X-axis logarithmic.
weird but ok

[math] \displaystyle
y = t \\
x = t \\
x_{log} = \log t \\
t = y = 10^{x_{log}} \\
[/math]
and this is how you do the second

[math] \displaystyle
y = t \\
x = t^2 \\
x_{log} = \log t^2 \\
t = y = \sqrt{ 10^{x_{log}} }
[/math]

[Anonymous No.15110039]

>>15099327
Hey anon, how do you approach the proof for function for this problem? I'm not entirely sure because we aren't given anything. Can you give some hint?

[Anonymous No.15110146]

>>15109718
I see what you are doing here, you are solving for t. But I don't think the result is correct. Here is what semilogx for y=x^2 looks like.
y(10^2) = 10000.
But for y=sqrt(10^xlog) let xlog=2 then y = sqrt(100)=10.

[Anonymous No.15110147]

>>15109718
Or another example: y= 1/(x+1).
if we solve for x, we will get y= 1/10^xlog - 1
But the proper result is y=1/(10^x+1), so we just take 10 to the power of x but the expression remains the same. Here are two graphs side by side

[Anonymous No.15110155]

>>15110146
>>15110147
oh fuck yea we way overthought this.
its (10^x)^2.
you just replace x with 10^x. you messed up 10^x^2 by not having parentheses. thats my bad man.

[Anonymous No.15110176]

>>15110155
Damn, thanks, you are right anon, I thought I tried all kinds of parentheses but maybe not. Now that x^2 is working, I am working up to the real one I wanted to test, y=20log10(1/sqrt(1+(x/w)^2)) which is a Bode plot expression for the magnitude part of a LPF transfer function where w is a constant (the cutoff frequency). I am going to drop 20log10 for now for simplicity and do strictly semilogx. Do you think it should be just
1/sqrt(1+((10^x)/w)^2) ?
I've been struggling with this one, couldn't get it right and tried all kinds of parentheses but maybe I've missed the right combination.

[Anonymous No.15110185]

>>15110176
yep, just tested, the full expression worked like a charm. i had no idea what i've been doing wrong, probably kept messing up the syntax.

[Anonymous No.15110187]

>>15110176
>I've been struggling with this one, couldn't get it right and tried all kinds of parentheses but maybe I've missed the right combination.
iunno looks right to me
>>15110185
nvm then

[Anonymous No.15110195]

>>15110187
Mine works fine for w=1, but I think something is off, yours looks perfect. I will keep tweaking. What did you type to get log10 with a subscript? I use log, hopefully it is the same as log10, since there is also ln (matlab doesn't understand ln so log=ln and there is also log10, it is a mess).

[Anonymous No.15110200]

>>15110195
Ah an underscore just like in Latex.

[Anonymous No.15110206]

>>15110187
Aaaa I am retarded I wasn't paying attention I had a typo, now I compared with your screen and everything is working perfectly. I bet that's what happened earlier, I always make stupid typos and then pull hair for hours. Ugh. OK I am done for the day. Thanks anon.

[Anonymous No.15110207]

>>15110195
>(matlab doesn't understand ln so log=ln and there is also log10, it is a mess)
mathematicians only care about log base e and some of them even look down on writing ln. they just cant handle the chad engineers using different log bases.
technically all logarithms differ by a constant scalar, but do you really want to write log(10)^-1 in front of all your expressions?
>>15110206
np anon, sorry i was retarded at first. this was definitely my most embarrassing blunder.

[Anonymous No.15110445]

Can someone explain non verbal autistics to me?
I'm a bit confused because I've read that they can't speak, they can't write, they can't use touch pads to communicate and they can't use facilitated communication
Any evidence of the above being possible is bullshit and disproven
Based on this I just can't really contemplate what kind of individuals they are, they seem like vegetables that move to me
Lets say I had a non verbal autistic son and it was dinner time, I could hear his stomach rumbling
If I said 'dinner's ready' would he get up and try to go to the kitchen?
Or would he need to see the food to get up?
Or can they do neither of these things?

[Anonymous No.15110506]

>>15110207
>mathematicians only care about log base e and some of them even look down on writing ln
I just use "log" for the logarithm base e because I think "ln" is a dumb symbol and whoever invented it ought to be ashamed. Most elementary trascendetal functions use three letters for their symbols (like sin, cos, tan, exp, log) so why would you use only two letters for the natural logarithm? We should just write "lgn" instead of "ln" if we need a different symbol for the natural logarithm, but I'm guessing nobody uses that notation.

[Anonymous No.15110613]

Is a core density in the order of 10^12 g/cm^3 normal for a star with a mass of 10 solar masses?

[Anonymous No.15110621]

>>15108776
ty

[Anonymous No.15110731]

Why is complex analysis easier than real analysis?

[Anonymous No.15110741]

>>15110613
That sounds insanely high and is approaching neutron star density.

[math]
\begin{array}{|c|c|}
\hline \text{Fusion phase}&\text{Mean density (g/cm}^3)\\
\hline \text{Hydrogen} & 5\\
\hline \text{Helium} & 700\\
\hline \text{Carbon} & 200,000\\
\hline \text{Neon} & 4,000,000\\
\hline \text{Oxygen} & 10,000,000\\
\hline \text{Silicon} & 30,000,000\\
\hline
\end{array}
[/math]

[Anonymous No.15110760]

>>15110731
It's not especially once you go into multivariable complex functions.

[Anonymous No.15110853]

>prove that if [math]a_n >0[/math] then [math]\displaystyle \lim _{n \to \infty} x_n = (1 + a_1)(1 + a_2)...(1+a_n) \in \mathbb{R} \iff \sum ^{\infty} _{n =1} < \infty[/math]
Any hints? I tried to play around with Am-Gm inequalities and partial sums but couldn't get anywhere

[Anonymous No.15110901]

>>15110853
meant to type [math]\displaystyle \sum ^{\infty} _{n = 1} a_n < \infty[/math]

[Anonymous No.15110908]

Is there an extension for matrix notation to non linear functions? Something like:
[math] \mathbf f^{ \mathsf T} \mathbf x = [ f (x_i) ]_i [/math]

[Anonymous No.15110912]

>>15110901
If [math]\displaystyle \sum_{n = 1}^{\infty} a_n < 1[/math] then you have that the geometric series [math]\displaystyle \sum_{k = 0}^{\infty} \left( \sum_{n = 1}^{\infty} a_n \right)^k[/math] is also finite, and it should be larger than [math]\lim_{n \to \infty} (1 + a_1) \ldots (1 + a_n)[/math]

[Anonymous No.15110925]

>>15110853
>>15110912
Wait, just remembered the normal way to prove that.
[math]\log( \lim_{n \to \infty} \prod_{k = 1}^{n} (1 + a_k)) = \sum_n^{\infty} \log ( 1 + a_n) \leq \sum_{n = 1}^{\infty} a_n[/math]

[Anonymous No.15110934]

Is the finite intersection of intervals is always an interval when it's nonempty?

[Anonymous No.15110935]

>>15110925
damn I wouldn't have thought of that in a hundred years. thanks

[Anonymous No.15110941]

>>15110934
*closed interval

[Anonymous No.15110948]

>>15110935
I've left enough gaps in there for you to sort out.
You should also try your hand at completing the geometric series proof.
>>15110934
Yes.

[Anonymous No.15111119]

Scientifically, how do I get a catfish Eirin gf?

[Anonymous No.15111130]

>>15111119
scientifically speaking 2d girls aren't real and you have mental issues.

[Anonymous No.15111200]

>>15110741
Thank you Anon. What do you think would be a reasonable density for such a star?

I have a tread over at >>>/wsr/1303662 more or less about this

[Anonymous No.15111208]

>>15110934
>>15110941
In general, for an associative operation (like intersection), you can often show it has some property for finitely many arguments by just showing it for two arguments, then extend using associativiry and a simple induction.

[Anonymous No.15111213]

>>15111200
> What do you think would be a reasonable density for such a star?
There's no one answer for that as it depends what stage in the star's life cycle it's at but since > 95-99% of any stars existence they are fusing H or He then I'd it to be fairly low (though higher mass stars will have higher core densities).

[Anonymous No.15111219]

Is the series [math]\frac{(-1)^n}{(-1)^n + n^a}[/math] convergent or divergent for [math]a \in (0,2)[/math]?
Trying to figure this out. Leibnitz doesn't work

[Anonymous No.15111224]

is there a name for the class of functions whose primitive you can write using only elementary functions? (for example [math] e^{-x^{2}} [/math] wouldnt be in this class

[Anonymous No.15111259]

>>15105118
>for finding the direction of the torque I'm making the cross product between the force/weightforce I apply and the angular momentum (see example 2)
You take the cross product between the position vector to the the point that the force is applied and the force vector itself. The sum of torques is equal to the time derivative of angular momentum, but angular momentum doesn't enter into the calculation of the torque itself.

[Anonymous No.15111262]

>>15111224
Exponents are defined to be an elementary function so whatever list of functions you are allowing would be some class you made up yourself.

[Anonymous No.15111294]

>>15111219
the sequence or series (sequence of partial sums)?

[Anonymous No.15111296]

Why is P closed under karp reduction?

[Anonymous No.15111319]

>>15111219
[math]\dfrac{(-1)^n}{(-1)^n + n^a} \dfrac{n^a - (-1)^n}{n^a - (-1)^n} = \dfrac{(-1)^n n^a - 1}{n^{2a} + 1} = \dfrac{(-1)^n n^a}{n^{2a} + 1} - \dfrac{1}{n^{2a} + 1}[/math]. The first term always converges by alternating series and the second one only converges for [math]a > 0.5[/math]

[Anonymous No.15111328]

>>15111262
not sure if i misunderstood your post but i just meant that you cant write a primitive of the function i posted using only elementary functions. So [math] e^{-x^{2}} [/math] wouldnt be in the "class" but [math] e^{2x} [/math] would because you can easily find a primitive of it and express it using only elementary functions ([math] e^{2}x^{2} * 1/2 +c [/math]

[Anonymous No.15111385]

>>15111296
Nevermind, I got it, it was pretty obvious, however I don't quite get the case for why PSPACE is closed

[Anonymous No.15111440]

>>15111213
Alright, thank you.

[Anonymous No.15111762]

Stupid question:

[math]x(t) = Ae^{i\omega t} + Be^{-i\omega t}[/math] is the general solution for a simple harmonic oscillator.
I've read that because [math]x(t)[/math] is a real function, [math]A[/math] and [math]B[/math] have to be complex conjugates of each other. I don't see how this follows.

Also, please explain how picrel follows. I don't understand that either. I get that [math]A[/math] and [math]B[/math] have to be related in some way for the sum to be a real number, but I don't see why they have to be complex conjugates exactly.

[Anonymous No.15111824]

>>15111762
Consider A=a+ci and B=b+di such that A is not the complex conjugate of B, and expand out the right-hand side of your equation using the substitution [math]e^{ix}=\cos{x}+i\sin{x}[/math].

[Anonymous No.15111830]

>>15111762
Consider A=a+ci and B=b+di such that A and B are not complex conjugates of each other, and rewrite your equation using Euler's exponential formula

[Anonymous No.15111849]

>>15111762
> A and B have to be complex conjugates of each other. I don't see how this follows
[math]\begin{align}
x(t) = Ae^{i \omega t} + B^{-i \omega t} &= A(\cos{\omega t} + i\sin{\omega t}) + B(\cos{\omega t} - i\sin{\omega t}) \\
&= (A+B)\cos{\omega t} + (A - B) i\sin{\omega t}
\end{align}[/math]

Then if [math]A = a + ib[/math], and you assume that [math]A = B^*[/math] then [math]A+ A^* = 2a[/math] and [math]A - A^* = 2ib[/math]. So you obtain:

[math]\begin{align}
x(t) &= (A+B)\cos{\omega t} + (A - B) i\sin{\omega t} \\
&= (A+A^*)\cos{\omega t} + (A-A^*) i\sin{\omega t} \\
&= 2a \cos{\omega t} - 2b \sin{\omega t} \\
&= C \cos{\omega t} + D \sin{\omega t}
\end{align}[/math]

where C and D are real and hence so is [math]x(t)[/math].

[Anonymous No.15111854]

>>15111762
z is real iff im(z) = 0

And im(z) = ( z + \bar{z} ) / (2i) .

Use the fact that \bar{zw} = \bar{z}\bar{w} .

Here \bar{z} means complex conjugate of z

[Anonymous No.15111868]

Why is it that cos(4.7123)=0 but acos(0)=1.5708?
How can I get my 4.7123 back?

[Anonymous No.15111900]

>>15111868
You don't. [math]\cos(\theta + n\pi) = \cos(\theta)[/math]. So when you take the inverse you only get [math]\theta[/math].

[Anonymous No.15111909]

>>15111849
Ahhh alright, I get it now. [math]A-B[/math] needs to be entirely imaginary (so their real parts must be the same) and [math]A + B[/math] needs to be entirely real so their imaginary parts must be negatives of each other.
Thanks.

[Anonymous No.15111913]

>>15111900
I need that 4.7123 back though. Is there literally no way to get it back, even without the acos?

[Anonymous No.15111915]

>>15111913
You can add on multiples of π.
But there is no way to recover it specifically just from the knowledge of what the value of cos is.

[Anonymous No.15111928]

>>15111915
welp. Thanks anon

[Anonymous No.15112039]

>>15111909
>>15111849
wait, no, i don't get it, why do they _have_ to be complex conjugates, although complex conjugates do work?
But it's fine, I've found a different argument. A and B being complex conjugates leaves us exactly enough freedom for the real and imaginary parts of A to be arbitrary quantities, and so C and D can be any arbitrary constants, and therefore that's the general solution to the ODE.

[Anonymous No.15112073]

>>15112039
Letting ωt=z because it's easier to type:
[eqn](a+bi)(\cos{z}+i\sin{z})+(c+di)(\cos{z}-i\sin{z}=a\cos{z}+ai\sin{z}+bi\cos{z}-b\sin{z}+c\cos{z}-ci\sin{z}+di\cos{z}+d\sin{z}[/eqn]
[eqn]=(a+c)\cos{z}+(d-b)\sin{z}+(a-c)i\sin{z}+(b+d)i\cos{z}[/eqn]
Observe that the imaginary terms here cancel out iff a=c and b=-d, i.e. they are conjugate.

[Anonymous No.15112086]

>>15112039
> why do they _have_ to be complex conjugates
It's the only solution to (A + B) and i(A - B) both being real. Write out the components and you get a set of 4 simultaneous equations with only a single answer.

[Anonymous No.15112146]

I don't understand this question.
I haven't done algebra in a decade and I was bad back then.
I don't get why my answer is wrong.
I s

[Anonymous No.15112154]

>>15112146
The y-axis is defined by the line x=0.

[Anonymous No.15112160]

>>15112146
Coordinates are (x,y), not (y,x).

[Anonymous No.15112418]

I'm trying to use the Residue Theorem to evaluate the integral for x ranging over the real line of cos(kx) / (x^2 + 1) dx , where k is a real constant .

However , the answer I get is pi * exp( - k ) ,
whereas I know it should be something like pi * exp( - |k| ) . Could anyone explain where the absolute value comes from?

[Anonymous No.15112419]

>>15112418
Never mind, I am retarded.

[Anonymous No.15112469]

>>15111913
it is kind of like asking how many times did i run around the circle if i only remember where i stopped.

[Anonymous No.15112591]

>>15110731
because it's elegant and internally consistent

[Anonymous No.15112846]

why are there so many frog threads?

[Anonymous No.15112984]

>>15104536
let A be an uncountable subset of R and bounded below. How to define an uncountable subset of A such that its infimum is bigger than the infimum of A?

[Anonymous No.15113346]

scientifically speaking why can't I read the clock moments after waking up? it takes 5-10 seconds until the symbols or information makes sense.

[Anonymous No.15113929]

Is a one-hidden-layered feed forward neural network in which the number of hidden neurons equals the number of features and there is no activation function and the output layer only has one value the same thing as a linear model?

[Anonymous No.15114619]

how should you cope with failed problems
like problems you're sure you got correct and when you check the solution you're retarded and the solution makes perfect sense but you don't improve and you still fuck up the next problem set?

[noob No.15114725]

Could any anon please help me with this?
Whenever I try to pass a name as an argument, say function("Alex", &head, &tail), it says it expects a char, not a char (*)
also, in the original node, the variable "name" is declared as a char[10], so in strcmp, n->info.name is also considered a char (when im given the error message)
Obviously, I'm doing smth wrong but I can't tell what
How do i pass a full name to compare it to that part of the node? Thx in advance

[Anonymous No.15114728]

>>15112846
Crossboarders

>>15114711
Will you give your input on /sci/'s 4chan cup roster

[Anonymous No.15114781]

test

[Anonymous No.15115027]

I was watching this:
https://www.youtube.com/watch?v=3gyHKCDq1YA

What does it mean for 1/3 to end in a 7 here?

[Anonymous No.15115052]

>>15115027
7 is the only single-digit number in base 10 that produces a final of 1 when multiplied by 3, so for the product to end in a 1 the number itself must end in a 7. There's no special significance of it being a 7 besides that.

[Anonymous No.15115080]

>>15115052
But does it relate in anyway to the real 1/3? Like can I think of 1/3 as ending in a 7?

[Anonymous No.15115105]

>>15115080
No. 1/3 is just an endless chain of 3s in proper decimal.

[Anonymous No.15115189]

If big monsters are real hypothetically, will they be slow because of gravity?

[Anonymous No.15115278]

>>15106003
Better as in...?
If you get tired after you eat, that can be a sign of Mc'Beetus.

[Anonymous No.15115328]

This is probably really simple but I can't find an answer online. I keep on applying it to rolling two dice (like how 7 is the most common) but I'm not sure.

Say I have a population that has two variables, x and y. Both variables are UNIFORMLY distributed. If I combine both variables (by adding them together) do I end up with a normal distribution?

So with the dice example you have an equal chance of getting a 1-6. But roll two dice and now 7 is the most common, 6 is second most, 5 is third most etc.

I know it's true for dice but can it be applied with everything?

[Anonymous No.15115416]

>>15115328
I believe yes, that is how normal distributions are made in the first place

[Anonymous No.15115418]

>>15115328
See Central Limit Theorem. You may also be interested in Poisson Limit Theorem.

[Anonymous No.15115463]

>>15115328
>If I combine both variables (by adding them together) do I end up with a normal distribution?
No. The PDF is either a trapezoid or (if both intervals have the same width) a triangle. The set of possible pairs forms a rectangle in the plane; the probability density is uniform across the rectangle. The set of pairs whose sum is a given value forms a diagonal line. The probability density of the sum is proportional to the length of the line segment obtained by intersecting the line with the rectangle.

For three variables, the probability density is the area of the intersection of a plane with a cuboid, so it has up to 8 points (7 intervals) rather than 4 points (3 intervals) and will look a bit more like a bell curve. The first and last intervals will be quadratic rather than linear. A normal distribution arises from the sum of an infinite number of uniformly-distributed variables.

[Anonymous No.15115483]

>>15115416
Thanks!
>>15115418
>Central limit theorem
I think this is what I was looking for. Wikipedia says
>when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
So surely that explains that I'm right?

>>15115463
Okay a lot of this is going over my head. I didn't do maths at university (doing medicine) but like doing maths as a hobby.
>A normal distribution arises from the sum of an infinite number of uniformly-distributed variables.
Are you saying that it won't be a normal distribution because that would require a (theoretically) infinite sample size? I thought in practice you can just call it a normal distribution even if the sample size is small.

[Anonymous No.15115486]

>>15104536
the master spark i that marisa pic is a heptagon the correct one is an octagon, i also think the bagua that's missing from it is (xùn), could be wrong though

[Anonymous No.15115499]

>>15115483
>>15115463
Oh I think i understand. You're saying that with just the two variables it would look more like a pyramid. But introduce more variables, and it would eventually tend towards a bell curve?

[Anonymous No.15115574]

What kinds of sets does the Axiom of Choice allow to be well-ordered that wouldn't be well-orderable otherwise? I know the real numbers would be one of those but is there a general term for such sets?

[Anonymous No.15115655]

Does the Dzhanibekov effect (aka Tennis Racket effect) play any role in knife throwing?

[Anonymous No.15115791]

>>15115499
Yes.

[Anonymous No.15115827]

>>15104536
I feel like every first or second thread here nowadays belongs here. Fuck this board has gone to shit

[Anonymous No.15115841]

>>15115483
Also if [math] F^R [/math] is the right inverse of a CDF of a continuous distribution and [math] U [/math] is a standard uniform random variable than [math] F^R \circ U [/math] is a random variable with CDF [math] F [/math]. So [math] \Phi^{-1} \circ U [/math] is standard normally distributed where [math] \Phi [/math] is the CDF of a standard normal variable.

[Anonymous No.15116120]

>>15115328
>I know it's true for dice but can it be applied with everything?
Normal distribution is continuous. How can anything to do with dice scores follow a continuous distribution (except in the limiting sense)?

[Anonymous No.15116178]

I know an alternate way to write a univariate OLS estimator is [math]\hat{\beta} = \frac{Cov(x,y)}{Var(x)}[/math], but is there an equivalent formulation for multivariate OLS? Is it the inverse of the variance-covariance matrix times a vector of covariances?

[Anonymous No.15116196]

The negation of "a set is uncountable" is not "a set is countable" but "a set is either countable or finite" right?

[Anonymous No.15116204]

>>15116196
Almost. It can also have a power equal to some infinite set that is higher than R

[Anonymous No.15116214]

>>15116204
A set with a cardinality higher than [math]\mathbb{R}[/math] is still considered uncountable, though. No differently than how it's still infinite even though it would also be greater in cardinality than [math]\mathbb{Z}[/math]

[Anonymous No.15116216]

>>15116178
[math]\beta = X^+ y[/math], where [math]X^+[/math] is X's Moore-Penrose inverse. If [math]X'X[/math] is invertible (that is, if [math]X[/math] is injective) then you have [math]X^+ = (X'X)^{-1}X[/math]

[Anonymous No.15116220]

>>15116214
This is a terminology dispute more than anything but usually uncountable means of power equal to R in my experience.

[Anonymous No.15116240]

Whats the best compression algorithm for terabytes worth of very similar decimal point numbers, lossless or not but with a predictable error no bigger than .001%.

[Anonymous No.15116278]

>>15116216
Right, that's the standard OLS estimator. What I'm asking is if it's valid to say that

[eqn]
\hat{\beta} = (X'X)^{-1}X'y =
\begin{pmatrix}
Var(x_1) & Cov(x_1,x_2) & \cdots & Cov(x_1,x_n)\\
Cov(x_2,x_1) & Var(x_2) & \cdots & Cov(x_2,x_n)\\
\vdots & \ddots & \ddots & \vdots\\
Cov(x_n,x_1) & Cov(x_n,x_2) & \cdots & Var(x_n)
\end{pmatrix}^{-1}
\begin{pmatrix}
Cov(x_1,y)\\
Cov(x_2,y)\\
\vdots\\
Cov(x_n,y)
\end{pmatrix}
[/eqn]

[Anonymous No.15116340]

>>15116178
It's incorrect to call it covariance and variance, since x is constant.
The formula you gave is only true for the slope coefficient. Also, on a related note:
[math] \operatorname{var-cov} [ \hat{ \mathbf \beta} ] = \sigma^2_u ( \mathbf X^{ \mathsf T} \mathbf X )^{-1} [/math] where [math] \sigma^2_U [/math] is the (constant) error variance.

[Anonymous No.15116344]

[eqn]\sum ^\infty _{n = 1} (-1)^n (\sqrt[n]{n} - 1)^n \\
\sum ^\infty _{n = 1} \frac{(-1)^{\lfloor \ln{n} \rfloor}}{n}
[/eqn]
How do I deal with these pieces of shit?
for the first one I figured out that [math](\sqrt[n]{n} - 1)[/math] is decreasing but I don't know how to deal with the power of n
The second one seems impossible

[Anonymous No.15116372]

What do actual scientists in this thread think of the consciousness as fundamental crusade and all the idealistic drivel in so many threads on /sci/ nowadays?

[Anonymous No.15116378]

can anyone recommend a print on demand service?

[Anonymous No.15116469]

Can protein folding be used as proof of work in a crypto algorithm?

[Anonymous No.15116472]

>>15115278
More energetic, easier to focus, more curious etc. Just better on every level. Maybe some specific food is causing it, just had chicken and potatoes and I feel good. I'll cut bread for now and see what's up.

>>15108955
Makes sense but it's also been inconsistent for me. Who knows.

[Anonymous No.15116493]

i ate like constant shit for like 4-5 years and now I'm changing to a healthier diet, and cutting out all the sugar and caffeine (although I still had a fair bit just because this worried me, still far less than usual) immediately is making me feel fucking dead. Is this normal as my body adjusts?

[Anonymous No.15116496]

>>15116493
>cutting out all the sugar and caffeine
retarded. learn moderation.

[Anonymous No.15116499]

Do stochastic differential equations share the same solution set as their deterministic counterparts? For example, would these two SPDEs have no solution as well?
[eqn]\frac{ \partial y}{ \partial x_1} + i \frac{ \partial y}{ \partial x_2} + 2(x_2 - ix_1) \frac{ \partial y}{ \partial x_3} = F(x_1, x_2, x_3) + W(x_1, x_2, x_3)[/eqn]
for non-analytic [math](0,0)[/math]
[eqn]\frac{ \partial z}{ \partial x} + i \frac{ \partial z}{ \partial y} = F(x,y) + W(x,y)[/eqn]
for non-analytic [math](0,y)[/math]
where [math]F[/math] is the differential operator and [math]W[/math] is the white noise.

[Anonymous No.15116596]

>>15116372
>>15116372

bumping

i want to know what people generally think of it since no one wants to contest people who just use buzzwords, so I figure I'll get an idea of if it's actually agreed on or not if I ask as someone not into it

[Anonymous No.15116609]

>>15116372
I don't give a shit, newfag.

[Anonymous No.15117290]

anons, water(liquid) changes to water(gas) at 100°C, so how the fuck are clouds formed cause I don't see any oceans or rivers boiling?

[Anonymous No.15117295]

>>15117290
Evaporation, which is not the same thing as boiling.
If you leave water out for some time, some of the molecules on the surface will slowly absorb enough heat from its surroundings to become a gas, gradually reducing the amount of water you have sitting around.
Boiling, in contrast, is directly applying the heat to the water, forcing it all to start evaporating, making it substantially faster.

[Anonymous No.15117369]

>>15117295
so anon, why does boiling water start changing into steam at 100°C, why isn't this achieved at let's say 40-50°C?

or is it that the water starts to change it state at 40°C or so and the temp of 100°C is required to completely change let's say 1L of liquid water into steam?

[Anonymous No.15117387]

>>15117369
Pressure.
Every liquid has an associated vapour pressure: it boils when this pressure is equal to that of the atmosphere "trying to keep it in place", so to speak, which is at 100 degrees Celsius for water. Water can evaporate at virtually any temperature so long as it isn't frozen, but it only boils when it's hot enough that it all can counteract the pressure of the atmosphere. That's also why boiling points go down the higher you go from sea level.

[Anonymous No.15117414]

>>15104536
ok champs, here is a problem that took me some a while

>What natural number less than 1000 has the most factors?

You need to prove you're correct.

[Anonymous No.15117426]

>>15117414
How is that hard? Just write some code to test the first 1000 numbers.

[Anonymous No.15117427]

>>15117387
really thanks anon, got it

[Anonymous No.15117460]

>>15117414
You want the greatest variety of prime factors to maximize the number of combinations. You also want the smallest-sized primes. 2*3*5*7*11=2310 is greater than 1000, but 2*3*5*7=210 is not. You have room for an additional *3, or an additional *2*2. The latter results in more combinations (32 factors).

As the largest prime factor (7) may be replaced by multiple smaller factors, it's worth trying numbers whose factors only include multiples of 2, 3, and 5. However, the increased numbers of twos and threes don't match the drastic increase from introducing a seven.

Not really a proof. More a clunky approach.
Number is 840, I expect.

[Anonymous No.15117476]

>>15117426
>code
the point is to use your brain

>>15117460
>You want the greatest variety of prime factors to maximize the number of combinations. You also want the smallest-sized primes. 2*3*5*7*11=2310 is greater than 1000, but 2*3*5*7=210 is not.
Yeah but how do you prove that it has to be this product 2*3*5*7? Why not 2*3*5*11 for example?

>You want the greatest variety of prime factors to maximize the number of combinations. You also want the smallest-sized primes
You're absolutely right, but you need to prove this holds for any situation, that's the hard part

>As the largest prime factor (7) may be replaced by multiple smaller factors, it's worth trying numbers whose factors only include multiples of 2, 3, and 5. However, the increased numbers of twos and threes don't match the drastic increase from introducing a seven.
Or any other factor, right. The issue i'm having really is proving the product has to be 2*3*5*7 and not something else

Attempting all products is really messy

[Anonymous No.15117512]

>>15117476
>Why not 2*3*5*11 for example?
because there will be less combinations using 11 that are < 1000

>>15117460
> Number is 840, I expect.
It is.

[Anonymous No.15117589]

I'm trying to create a command in [math]\LaTeX[/math] that writes [math]\text{gcd}(a,b)[/math].
I tried \newcommand{\gcd}[2]{\text{gcd}(#1,#2)}, but when I use the comand it outputs [math]\text{gcd}(a,b,)[/math].
how can I get rid of that last comma?

[Anonymous No.15117602]

>>15117589
I bet you are using it incorrectly: gcd(a,b) instead of gcd{a}{b}

Also the command seems redundant.

[Anonymous No.15117607]

>>15117602
>gcd(a,b) instead of gcd{a}{b}
what do you mean

[Anonymous No.15117612]

>>15117602
because if you write \gcd(a,b) you will get the wrong output you described since that's the same as writing \gcd{a,b}{}

[Anonymous No.15117613]

>>15117607
because if you write \gcd(a,b) you will get the wrong output you described since that's the same as writing \gcd{a,b}{}

[Anonymous No.15117614]

>>15117613
I see. just tried it, it worked, thanks!

[Anonymous No.15117798]

Can switching null and alternative hypothesis change the conclusion?

[Anonymous No.15117882]

>>15117589
LaTeX already has a GCD command.

[Anonymous No.15118060]

>>15117512
>because there will be less combinations using 11 that are < 1000
This doesnt prove there won't be a number that has more factors since the number of factors only depends on the exponents

[Anonymous No.15118123]

>>15116344
The first series is trivially absolutely convergent since the nth root goes to 0.

[Anonymous No.15118570]

>>15116472
Might have solved it, I was eating about 100g of 28% cheese (that's almost 350 calories) and maybe it's caused by tryptophan. Haven't had cheese today and felt ok.

[Anonymous No.15118651]

>>15116344
funny pattern i noticed when thinking about the second one:
[math] \displaystyle
\lfloor \ln 1 \rfloor = 0 \\
\lfloor \ln 2 \rfloor = 0
[/math]
so theres two zeros.
[math] \displaystyle
\lfloor \ln 3 \rfloor = 1 \\
\lfloor \ln 4 \rfloor = 1 \\
\lfloor \ln 5 \rfloor = 1 \\
\lfloor \ln 6 \rfloor = 1 \\
\lfloor \ln 7 \rfloor = 1
[/math]
five ones.
then theres 13 twos.
at this point i made a prediction that there would be 34 threes, and there were!
do you see why? its every other fibbonaci number. 1 1 2 3 5 8 13 21 34 55 89 ...
so i then made a prediction that were are 89 fours, and boy was i disappointed when there was 94 :(

[Anonymous No.15118655]

>>15118651
https://en.wikipedia.org/wiki/Strong_law_of_small_numbers

[Anonymous No.15118660]

how much of an effect is there on the brain if you read a lot isn't there something where taking the perspective of another people through reading trains up certain social abilities

[Anonymous No.15118766]

What are those "types" the HoTT people talk about? Does it have anything to do with the set-theoretic concept (afaik, of a set [math]A[/math] with a well-ordering [math]R[/math], its type is the smallest ordinal [math]\alpha[/math], such that [math](A;R)\cong (\alpha;\in)[/math])?

[Anonymous No.15118862]

What's the best way to convert a high dpi scan of a textbook to black and white vector image?

[Anonymous No.15118879]

>>15118766
I’m confused. If two given ordinals are isomorphic as ordered sets, then aren’t they necessarily equal? So, wouldn’t there be exactly one ordinal for each well ordered set A? (So the word “smallest” is redundant.)

[Anonymous No.15118905]

>>15118862
/g/ will be a better place to ask that

[Anonymous No.15118954]

>>15118879
You're right, the ordinal would be unique (specifically since I specified a well-order relation).
I think I only said "smallest" since, when using shorthand notation, say [math]\operatorname{type}(\mathbb{N})[/math], you're usually not thinking of the relation that well-orders it to be [math]\{2,3,4,...,1\}[/math], which would imply [math]\operatorname{type}(\mathbb{N})=\omega +1[/math], but rather the usual one, for which it's just [math]\omega[/math].

[Anonymous No.15118976]

was reading a textbook and saw this:
[eqn](-1)^k \cos{2k} = \cos{((\pi - 2)k)}[/eqn]
Why is this true? I don't understand

[Anonymous No.15118988]

>>15118976
if k=2n:
[math]\cos((\pi-2)k)=\cos(\pi{2n}-2(k))=\cos{2n\pi-2k}=\cos{2k}[/math]
if k=2n+1:
[math]\cos((\pi-2)k)=\cos(\pi{2n+1}-2k)=\cos{2n\pi+\pi-k}=\cos{\pi-2k}=-\cos{2k}[/math]

[Anonymous No.15118991]

>>15118988
Pretend there are parentheses around all of the terms follow [math]\cos[/math]. I'm not sober enough to double-check my own typing

[Anonymous No.15118998]

>>15118988
ok i kind of see it now

[Anonymous No.15119072]

I am not sure where to ask this question. I had a really vivid dream today where I was fighting in Iraq and eventually got killed. I have never been to Iraq. Anyways, I am wondering when people 'hear' things or 'feel' things in a dream, is their brain just hallucinating sounds or is it something deeper?

[Anonymous No.15119102]

>>15118976
related question:
is there some simple rule to take a (-1)^n from under a cos or a sin?
i have noticed several examples of this now but I don't "see it" so to speak

[Anonymous No.15119114]

I taking intro numerical methods, but I feel like I'm getting filtered
like the fuck even is Simpson's rule?
any book recommendations to help me?

[Anonymous No.15119116]

>>15119102
cos is an even function, so cos(x)=cos(-x)
sin is an odd function, so sin(x)=-sin(x)
So, yes, if you can separate into cases based upon the value of (-1)^n. Otherwise, no.

[Anonymous No.15119120]

>>15119102
If you're willing and able to split it into cases based upon what value (-1)^n takes, then yes.
cos is an even function, so cos(-x)=cos(x)
sin is an odd function, so sin(-x)=-sin(x)
But if you can't use cases, then no.

[Anonymous No.15119144]

>>15119120
i mean taking an expression and taking out a (-1)^n out of it
e.g. [math]\cos{(n\pi - \frac{n\pi}{n+1})} = (-1)^n \cos{(\pi - \frac{\pi}{n +1})}[/math] according to my textbook but this seems entirely non-obvious, at least not for me. maybe I'm bad at trigonometry but I would think that there could be some pattern. i know [math]\cos{(n\pi)} \equiv (-1)^n[/math] and the rest is an application of those retarded annoying expressions

[Anonymous No.15119524]

>>15116278
In some sense yeah. Your first formula for simple regression is only for the slope (beta_1), and also only if you either have included an intercept (beta_0) or centered your variables.
Under the same assumptions you have that X'X is the sample cov matrix and X'Y is cov(x,y). Please note all are sample statistics, not population.

[Anonymous No.15119570]

how can I show that the product of 3 consecutive integers is always divisible by 6?

[Anonymous No.15119609]

>>15119570
at least one of the integers will always have a factor of 2, and one will always have a factor of 3

[Anonymous No.15120257]

sorry if this sounds dumb
can a object directly interact with other objects, or only with forces.

[Anonymous No.15120287]

Sorry for the retard tier question.
>Khan Academy
>Precalculus
[math]\frac{7}{x+4} + \frac{3}{x+6}[/math]
I know how to solve these. You get a common denominator and then add like terms in the numerator. Afterwards, I got [math]\frac{10x + 54}{(x+4)(x+6)}[/math] and then factored a 2 from the numerator since 10 and 54 are both divisible by 2 and multiplication is associative, that is [math]10x = 2*5*x[/math]
My final answer was [math]\frac{2(5x + 27)}{(x+4)(x+6)}[/math], which they marked incorrect and said [math]\frac{10x + 54}{(x+4)(x+6)}[/math] was the correct answer. Why was my answer incorrect? I'm sure I'm making a retard tier mistake somewhere but I'm not seeing it. Sorry again.

[Anonymous No.15120328]

>>15120287
Your answer isn't incorrect per se, and it's stupid that it was marked as such, but it looks pretty weird to factor out a constant like that if you're not doing it to cancel something out

[Anonymous No.15120593]

>>15106588
Are you sure you didn’t mistype the question?

[Anonymous No.15120596]

>>15120287
Your answer‘s correct. The computer just didn’t expect you to factor out the 2.

[Anonymous No.15120657]

So I have been teaching the maths for CS to my nephew and I started with teaching him the 9 times table hand trick so he understands how to associate the numbers to the digits then I'm making sure he can use base 2 mentally so he can use the same technique to know what a string sums to. Are there any more maths tricks to know that can be easily taught that are not the exact concept but similar enough so he can process it easier?

[Anonymous No.15120736]

I hate probability so much, dumb this down for me.

"In this task, you should not only calculate but also give a reasonable representation of
probabilities, and make visible which rules you have used.

In a board game, you must roll dice to determine whether you pass or fail. Arne fights a monster and rolls two dice. A die is a "success" if it is 5 or 6. He must pass at least one success to win.

1. What is the probability of Arne winning the game?

Later, there is another match. Arne still has to throw two dice. However, he got some bonuses:
every 6 counts as a "double success" (5s still count as 'one success')

2. What is the chance, with these rules, that Arne gets 2 successes? 3 successes?"


As for question one, I assume this is 1/3 since one side of the dice is 1/6th chance, 1/6th + 1/6th = 2/6th = 1/3th chance, right?


But how do I go on about calculating question two?

[Anonymous No.15120767]

Should I get Tao's analysis I and II or baby rudin?

[Anonymous No.15120841]

>>15120657
don't teach him tricks, drill the tables then explain the concepts

i don't think most adults even know what is a place value, why base 10 has powers of ten for each place value (it's not "because it just it is")

[Anonymous No.15121131]

Good Morning /Sci/entists.

This feels like a good day for Computer Science. There is a lot of energy floating around to use books and computers.

>>15104563
>>15108404
All of the maid questions can be considered solved. Kurumi MaidCard has been released and a nice /sci/entist came and told me papers with ideas from Grzegorczyk Hierarchy. I am working on the Ilulu Number Calculator now. I will release it on a Maid Card when it completes. Soon everybody will be able to play with very big numbers. The Ilulu Number Calculator is partly written in SLAM so probably they will just be released together on the same Maid Card.

I might take a break from making Computer Programs to read the Geometric Magic Squares book because I like that it has drawings on it and I want to understand the Drawings and make my Computer draw them too.

I should also probably try to make a paper about Maid Space or something but I don't know how to sound like a good math writer.

Thank you /sci/entists for reading my post.

[Anonymous No.15121147]

>>15120767
Amann & Escher mogs them both.

[Anonymous No.15121151]

I want to learn more about genetics what maths will I need to better understand it?

[Anonymous No.15121186]

>>>/wsr/1306136

[Anonymous No.15121237]

thoughts on asking the ai questions instead of posting them here? i got satisfactory answers, but it might be confirmation bias, would it be?

[Anonymous No.15121278]

>>15121237
If you're confident enough in your grasp of the subject to double check the AI's answers, go right ahead.
Otherwise don't, AI can and will randomly spout nonsense.

[Anonymous No.15121299]

>>15121278
> AI can and will randomly spout nonsense.
to be fair i do that too

[Anonymous No.15121313]

>>15121278
>AI can and will randomly spout nonsense.
And /sci/ doesn't?

[Anonymous No.15121347]

>>15121237
If you got satisfactory answers from AI, your questions don't deserve to be here.

>>15120736
Your first part is wrong because you only consider the first roll. You are suppose to have AT LEAST ONE success in two rolls. So find a way to count all the ways you can have 5 or 6 in at least one of the two rolls, and divide it by the the number of possibility in 2 rolls.

One thing that makes classical probability questions easier is to reduce the problems into of tuples. For this problem, you can use a 2-tuple that represents the represents the result in the first and second roll respectively. So the number of elements in the sample space is 6 times 6 since there are 6 possibilities for the first place, and GIVEN any of those possibilities for the first place, there are additional 6 for the latter. You made the mistake of only counting the possibilities for one position. There are two possibilities for only one position, yes, but now you also have to consider the possibilities for the other position.

Sometimes you cannot multiply and you have to decompose them in to mutually exclusive tuples. Remember that you can add up the possibilities of mutually exclusive tuples. Now think how you can count tuples for your questions. Remember to consider ALL possibilities that pertain to the condition of your question.

For question 2, think how doubles successes can happen and how triple success can happen, and decompose them into mutually exclusive tuples.

Hint first part:
There are three ways the Arne can win:
1. He gets success in the first, but not the second.
2. Other way around.
3. Success in both.
Note these three ways are mutually exclusive, so count for each way and add them up. There is actually faster way to do this which doesn't require counting three way separately. Can you think of one?

Hint second part:
Getting exactly double successes is mutually exclusive to getting triple successes. So addition is valid.

>>15121313
Lol gottem.

[Anonymous No.15121382]

>>15104536
I first learned about the Planck distribution and the ultraviolet catastrophe, I had the idea that it demonstrated that the classical theory is wrong, and the quantum theory is true. But looking back on it, it seems like people couldn't come up with a valid classical theory in the first place.

The assumption that you have a black box in which standing waves of light could exist is extremely idealistic, and the notion that the energy would be distributed among the frequencies according to the equipartition theorem by modelling them as harmonic oscillators doesn't make any sense. Not only is it so that harmonic oscillators can still assume continuous angular momenta whereas for light it's restricted to integer values (because of the boundary conditions), the equipartition theorem gives the energy /per oscillator/; but again, calling the frequencies the oscillators is a conflation of terms. I just don't see how you can legitimately use thermodynamics if you don't assume light comes in quanta.

Does this criticism make sense, or is there more to the classical theory than I'm giving it credit for?

[Anonymous No.15121392]

>>15121382
>continuous angular momenta
continuous angular frequencies*

[Anonymous No.15121407]

>>15121382
And a bit of a related question: how should I think about light quanta in a spherical cavity? For standing waves it's easy enough to see that E = h f, but when you have spherical boundary conditions (which might be just as realistic as a rectangular box), the waves are found to be composed of spherical harmonics and Bessel functions. What are the quanta here?

[Anonymous No.15121443]

>>15121313
It also does but I usually double check other people's answers when I can.

[Anonymous No.15121491]

>>15121443
so
1. ask question in /sqt/
2. reply to your own post with the AI answer
3. wait for remi to check it
got it

[Anonymous No.15121662]

>>15104536
Is heat transfer a hard class?

[Anonymous No.15121686]

Is math a meme degree

[Anonymous No.15121719]

I don't get this question

>Write three examples of fractions that when written as a decimal, the decimal repeats indefinitely.
>Explain why it makes sense that each fraction is equivalent to that decimal.

Does it want me to say the division keeps going and that why it makes sense?

[Anonymous No.15121722]

>>15121686
Yes, go be a rancher/cowboy/plumber/paramedic/gardner/cook/firefighter/farmer/etc

[Anonymous No.15121833]

>>15120767
Rudin
>>15121147
Literally delusional. Please seek psychiatric help.

[Anonymous No.15121841]

>>15121833
Kys worthless deluded projecting scihzophreniac

>15120767
Read Springer

[Anonymous No.15121842]

>>15121833
Explain your reasoning

[Anonymous No.15121876]

>>15121719
I really have no idea how to solve this

[Anonymous No.15121927]

>it's another episode of show that XY is a vector subspace

[Anonymous No.15121990]

>>15121876
Stupid task.
You need you nominator to be 9, 99, 999 etc. then your numerator is the periodic number.
So 3/9=0.3333...
4/11=36/99=0.363636...
I guess that's what they're asking

[Anonymous No.15122047]

Metallurgical engineering

What do you say?

[Anonymous No.15122131]

>>15120328
>>15120596
Thanks anons. On closer inspection although I was algebraically correct, I was technically incorrect. They expressly did not want the numerator factored.
>The numerator should be expanded and simplified. The denominator should be either expanded or factored.
You know, before bothering you with this question I asked one of the AI chat bots—specifically the Mathematica offical CharacterAI bot—to help explain what, if anything, I was doing wrong, and surprisingly it spewed out a bunch of incoherent babble. For instance,
>Yes, 10x + 54 is equal to 2(5x + 27).
>This can be seen by doing the following:
>10x + 54 divided by 2 would be equivalent to 5x + 27.
>5x + 27 can be rewritten as 2(2.5x + 13.5).
>2(2.5x + 13.5) would be equal to 2(5x + 27), since the values of the constants equal to one another.
Previously I've used the CharAI bots to supplement learning history, and they'd almost never say anything so clearly incorrect, but their Math bot, in this instance, has been completely useless. I know CharAI have said their model is not a derivative of GPT but I wonder if GPT-4 will be able to tackle these sorts of questions more competently. I certainly hope so.
>it looks pretty weird to factor out a constant like that if you're not doing it to cancel something out
Ah, okay, thanks, I'll keep that in mind. I remember skimming through some of the Algebra lessons on Khan Academy and in all their exercises they seemed to stress results that can be factored must be factored, so I suppose it's just a bad habit. I'll try to refrain from factoring unless necessary to cancel or otherwise instructed to do so, though admittedly factoring is quite satisfying, especially with higher degree terms.

[Anonymous No.15122141]

how can I NATURALLY warm up my body while chilling on my pc?

[Anonymous No.15122179]

>>15122141
Drink hot drinks. Tea is nice. Earl Grey is nice. Green tea is nice. Coffee is also nice.

[Anonymous No.15122336]

following Eichler's proof of Baker-campbell-hausdorff, (proof can be found in Naive lie theory by Stillwell, John, pg157 or Introduction to lie groups and lie algebras
by Sagle, Arthur A,pg 133) but I can't seem to work out how relations (5) and (6) are combined like they say it is in the related picture (a section from the second source)

[Anonymous No.15122348]

>>15122336
rewriting 5 as -Fn(A+B,-B) for a bit more clarity:
they're substituting A=-X, B=(X+Y)

[Anonymous No.15122371]

>>15122348
oh, I see. I guess I was overcomplicating it involving lie congruences. Thank you!

[Anonymous No.15122549]

Can someone explain why the concept of "adding negative numbers" is taught in schools when it's literally the same exact operation as simple subtraction? Is it just so low IQ inner city niglets can understand subtraction better?
It just seems to make something simple more complex and muddled than it needs to be.

[Anonymous No.15122742]

>>15104536
How do I define an injection from [math]\mathbb{N}^2[/math] to [math]\mathbb{N}[/math]

[Anonymous No.15122851]

>>15121382
>The assumption that you have a black box in which standing waves of light could exist is extremely idealistic
Any wave with boundary conditions will result in standing waves. The electric field at the walls of any container, be it a box, sphere or whatever, has to be zero which forces you to have to use such boundary conditions in any model.

> the notion that the energy would be distributed among the frequencies according to the equipartition theorem by modelling them as harmonic oscillators doesn't make any sense
The assumption (back then) was that the equipartition theorem was valid for all classical systems so it seemed logical to apply it to such a model even if it was first derived for particles and not waves. There was nothing about harmonic oscillators in the original black body calculations, just the assumption that the equipartition theorem was valid and hence a Boltzmann Distribution of energies should be used. But you are right that this turns out to be a problem and is the fundamental cause of the "ultraviolet catastrophe".

> is there more to the classical theory than I'm giving it credit for?
Yes. The original classical calculations turned out to be correct apart from the function for the distribution. All Plank had to do was with his guess of quantized energy was to then calculate the new distribution function it would generate and then put it into the original calculations. When he did that he ended up with an equation that matched experiments.

>>15121407
Spherical boundary conditions make no difference since it does not affect how light moves.

[Anonymous No.15123000]

>>15122742
With Cantor’s first diagonal argument

[Anonymous No.15123008]

>>15104536
Pls give me your opinions: my exams are graded out of 32.
This exam was divided in two parts: one in November and one in a few days from now.
The one in November was worth 12 points max, this one is worth 20 points max (so this one is more important than the other one), for a total of 32
In the one in November I got a 7/12 which means barely pass. Now my options are either take only the second exam which means I could get at most a 27/32 (but more realistically a 22/32 knowing my capabilities)
OR instead of doing only the second part I can do the whole exam again but I already kind of forgot all the topics for the first part of the exam.

Regardless of what I choose I have the option to retake the whole exam in about one month from now and that's my last chance. What would you do anons? Consider that I can't spend too much time on this exam because I have two other exams coming up in the next week

[Anonymous No.15123121]

for what values of alpha does [math]\int_{0}^{\infty}\frac{e^\frac{-1}{x^2}}{x^\alpha(1+x^\alpha)}dx[/math] converge?
My problem is when x goes to zero. What I say is that the above function is asymptotic to [math] \frac{1}{x^\alpha} [/math], therefore converges when alpha<1. What the books says is that when the function goes to zero (from the right) it's asymptotic to [math]\frac{e^\frac{-1}{x^2}}{x^\alpha}[/math], which seems the exact same as what I said but with a missing step (is it?)
but then it concludes that therefore it converges for each [math]\alpha>0[/math]

the end result is that it converges for every alpha greater than 1/2, my result is 1/2<alpha<1

[Anonymous No.15123237]

>>15122549
realistically it's the exact opposite. there's no point in teaching subtraction as its own thing when it's just a special case of addition.

[Anonymous No.15123253]

>>15123121
>which seems the exact same as what I said but with a missing step (is it?)
When [math]x[/math] goes to minus infinity [math]e^x[/math] goes to zero, so I'm not sure why you're discarding the [math]\exp (-1/(2 x^2))[/math] factor when looking at the asymptotics, you just worsen the estimate.

[Anonymous No.15123277]

Maybe the wrong post, I am an freshman (electrical engineering). I don't know why but these days i am not able to read properly i have to read things 2-3 times carefully to actually interest its meaning and i am not facing any problem in maths or anything's, most it's with understanding complex English sentences. I have never faced this in my whole neither i have any head injuries. Could extreme anxiety be the reason for this problem ? Cause I have anxious about few things in my life for a while and i am also a big overthinkee


Pls help anons

[Anonymous No.15123324]

How to study Electromagnetism (calculus based) without learning mechanics (calculus based) i literally don't understand any shit after columb's law, like what to integrate in gauss law and taking elements and other shit

[Anonymous No.15123372]

>>15122851
Thanks for the answer.
>Any wave with boundary conditions will result in standing waves.
My point is that not every object with a blackbody spectrum is a neat black box. Take the sun: we know light bounces around and that it leaves following a blackbody spectrum (absorption lines notwithstanding). This seems to me an extremely chaotic environment in which it's very difficult to justify treating it as a container of standing waves.

>The assumption (back then) was that the equipartition theorem was valid for all classical systems so it seemed logical to apply it to such a model even if it was first derived for particles and not waves.
I see, but it was still a matter of blindly applying the equipartition theorem where there was no rigorous justification to do so. To wit the equipartition theorem applies to systems where energy scales with the square of a physical parameter, which can be velocity/momentum (for particles in a gas), or displacement (for a harmonic oscillator). I don't know the exact historical justification they gave for applying the theorem, but Wikipedia says
>This formula is obtained from the equipartition theorem of classical statistical mechanics which states that all harmonic oscillator modes (degrees of freedom) of a system at equilibrium have an average energy of k_B T.

[Anonymous No.15123376]

>>15123372
The equipartition theorem has the curse (or at the time, blessing) of not caring about the properties of the oscillator: no matter the angular frequency of the oscillator, the average energy is always k_B T. No inquiry into the tensile properties of light waves is needed, you just need to know that it indeed is an oscillator. But that still rests my other criticism: k_B T is the average energy /per oscillator/. In the classical blackbody derivation, this amount of energy is awarded for each discrete mode of light, not for each oscillator ("each wave"), as it should. Suppose I lived in 1900 I may have conceded that that applying the equipartition theorem looks plausible, the picture that you end up getting, of standing waves of light, is obviously different from that of an ensemble of harmonic oscillators.

[Anonymous No.15123385]

>>15123121
split the integral into two parts: from 0 to 1 and from 1 to infinty. For the second part the function f under the integral obeys e^-1/(1+x)^2a=<f(x)=<1/x^2a, so that part coverges only for a>1/2. For the first part do something similar, but first make a substitution: t=1/x, you will get a "polynomial" in t multiplied by e^(-t^2), you are integrating that over 1 to in finity, so it will definitely converge for any a>0 (the degree of the "polynomial" will be something like 2a+1, so probably that part should converge for a>-1/2 )

[Anonymous No.15123410]

there is no "nice" way of writing
[eqn]\int_0^{+\infty}e^{-\lambda(x+x^2)}dx,\,\,\,\, \lambda>0[/eqn]right?

[Anonymous No.15123438]

>>15123410
First complete the square in the exponent
[eqn] \lambda (x + x^2) = \left(\sqrt{\lambda} x + \frac{\sqrt{\lambda}}{2} \right)^2 - \frac{\lambda}{4} [/eqn]
Now do an u-sub
[eqn]u = \left(\sqrt{\lambda} x + \frac{\sqrt{\lambda}}{2} \right) [/eqn]
The remaining integral can be written nicely in terms of the error function.

[Anonymous No.15123476]

>>15123410
int_0^infty exp(-lambda x) =1/lambda

int_0^infty exp(-lambda x^2)=int_0^infty exp(- (sqrt(lambda) x)^2)=1/sqrt(lambda) int_0^infty exp(-t^2)=1/2 1/sqrt(lambda) 1/sqrt(pi)

[Anonymous No.15123481]

>>15123476
disregard this, I'm retarded, do what this anon said:
>>15123438

[Anonymous No.15123482]

>>15123372
> My point is that not every object with a blackbody spectrum is a neat black box.
Irrelevant. We are talking about an "idealised" black-body. It's the like the joke about physicists modelling a cow, first they assume it's a sphere. You are trying to calculate how temperate correlates to the frequency of light emitted so having a scenario you can calculate is always best. Yes. real objects are not perfect black-bodys so will differ slightly from the idealised case but the difference is typically so small as to be meaningless.

> This seems to me an extremely chaotic environment
The inner workings don't matter since the only think that does is the surface temperature. The Sun, or any star, are actually almost perfect black-bodys since they are nearly uniform, opaque, and non-reflective. There's nothing complicated about the light they emit, it directly comes from the energy they generate.

[Anonymous No.15123571]

[math]f :\; ]0, 1] \ni x \mapsto 1/(1 + xe^{\frac{i}{x^{2}}}) \in \mathbb{C}[/math]
[math]\lim_{\ x\ \to\ 0} f(x)[/math]

How do you evaluate complex limites? Is there maybe a "L'Hopital" for complex-valued functions?

[Anonymous No.15123645]

>>15123324
Bump

[Anonymous No.15123806]

is the remainder from dividing [math]x[/math] by [math]x^3 + x[/math] equal to [math]x[/math]? I forgot how this shit works

[Anonymous No.15123857]

>>15123571
e^(i/x^2) = cos(1/x^2) +isin(1/x^2), which is bounded, from there u can use ur usual limit laws to find the limit to be 1. l'hopitals should work if the function is holomorphic, but I don't think it helps here , (we don't have a 0/0 or inf/inf intermediate)

[Anonymous No.15123881]

>>15123571
You do it with a circle centered at 0 of reducing radius, it's going to have an angle but the angle should be irrelevant when evaluating the limit.

[Anonymous No.15124056]

Whatever happened to Geodakyan's theory of sex? It's always mentioned as a potential explanation for the emergence of sex, but there is so much research left to be done that has simply been neglected.

[Anonymous No.15124349]

>>15124056
>he believes in evolution
>in 2023

[Anonymous No.15124526]

>>15124349
so what do you believe in?

[Anonymous No.15124539]

>>15124526
No he's right evolution is a fraud. It was created in order that communism could have a foundational myth of progress to refer back to. As that is the premise of Marxism, that we exist in a time of social ignorance and barbarity, but that we will progress through stages of ignorance and arrived at the enlightened state of Communism at some point in the future. Darwin and Marx were in frequent contact to the point you could accuse them of being friends

[Anonymous No.15124542]

>>15124539
/pol/-tier nonsense and not what I asked

[Anonymous No.15124548]

>>15124542
>stop putting together facts and coming to sensible conclusions right now!
No.

[Anonymous No.15124559]

>>15104536
get rid of your parasites you freak

[Anonymous No.15124700]

I have an endomorphism that can be represented in respect to a certain basis with the following matrix: [math]\begin{pmatrix}
1& 0 &0 \\
0& 1& 0\\
0& 0 &0 \\
\end{pmatrix} [/math]
Then there are two questions, if this endomorphism is diagonalizable and if it is also orthogonally diagonalizable.
To the first one I said yes because well I have just found a diagonal matrix that rapresents the endormorphism, therefore it's diagonalizable by definition. To the second question I also said yes because the matrix is also symmetrical (and for a version of the spectral theorem an endomorphism is symmetrical if and only if it is orthogonally diagonalizable, and an endomorphism is symmetrical if it can be represented with a symmetrical matrix).

But my book says that it's only diagonalizable, not orthogonally diagonalizable, but i dont see why it wouldnt be

[Anonymous No.15124725]

>>15124700
It's not invertible, so it's not orthogonal and thus not orthogonally diagonalisable

[Anonymous No.15124811]

Let [math] \{x_{n}\} [/math] be a sequence of real numbers, such that [math] \dfrac{4n^{3}+1}{2n^{3}+n-1}\leqslant\mid x_{n} \mid \leqslant \dfrac{2n^{2}+n-1}{n^{2}+2n-2} [/math]

If [math] \lbrace y_{n}\rbrace_{n\in \mathbb N} [/math] is a Cauchy sequence, show that [math] \lbrace y_{n}x_{n}\rbrace_{n\in \mathbb N} [/math] is also a Cauchy sequence.

I don't know what to do.

[Anonymous No.15124847]

>>15124811
Use Hölder's inequality.

[Anonymous No.15124859]

>>15104536
Good Evening /Sci/entists.

I am working on getting SLAM (Stack Language for Anime Maids) into a a nice state for release via Maid Card, since Kurumi MaidCard solves my problem of how to share a project with a lot of source files without using Github.

SLAM has a file loader where you can save and load your session, or save what you did in your session as a Computer Program written in SLAM so you can run the program to get back in a previous state.

This text form of the Computer Program can get stored in a Maid Card.

Currently to use a SLAM program in a Maid Card you have to extract the card with Kurumi MaidCard, then run SLAM's file loader pointed at the extracted text.

I am debating making it where SLAM can just read Maid Cards as input directly. If you point SLAM at a Maid Card I am thinking the end result should be SLAM running every Computer Program it finds on the Maid Card, instead of extracting text.

Are there any downside of this design I am not seeing?

Thank you /sci/entists for reading my post.

[Anonymous No.15124951]

>>15123806
Yeah.
>>15124700
>an endomorphism is symmetrical if and only if it is orthogonally diagonalizable, and an endomorphism is symmetrical if it can be represented with a symmetrical matrix).
Correction: it's symmetrical if it can be represented with a symmetrical matrix in an orthogonal basis.
Otherwise diagonalizable would always imply orthogonally diagonalizable.
>>15124811
L'Hospital, squeeze theorem, convergent implies Cauchy.

[Anonymous No.15124958]

>>15124951
>L'Hospital, squeeze theorem, convergent implies Cauchy.
Correction: L'Hospital, squeeze theorem, Cauchy implies convergent, product of convergent sequences is convergent, convergent implies Cauchy.

[Anonymous No.15125042]

>>15124958
Correction: L'Hopital
well, actually L'Hôpital

[Anonymous No.15125045]

>>15125042
the ô represents that it used to be "os", so l'Hospital is an archaic but correct way of writing it. certainly moreso than l'Hopital

[Anonymous No.15125093]

>>15125042
ロピタル

[Anonymous No.15125210]

>>15123482
>There's nothing complicated about the light they emit, it directly comes from the energy they generate.
The light that is assumed to be standing waves and have an integer number of waves in all three spatial dimensions, even though the light is generated in a hot, sloshing, opaque plasma? You really don't see the difference between such an obviously wrong underlying assumption for the theory, and a back-of-the-envelope approximation like with spherical cows? The quantum theory doesn't posit anything of the sort and manages to be right, so how can this picture be anything but wrong? Oh well, I think I've found my answer, thanks for the discussion.

[Anonymous No.15125250]

>>15125210
> You really don't see the difference
No, there really isn't. They are both emit black-body radiation. The mechanism that generates the light is immaterial however one scenario is much simpler to calculate than the other.

> You really don't see the difference between such an obviously wrong underlying assumption for the theory
No one is saying using the equipartition theorem was correct but that was just a single part of the model used. It was replaced by Planck's idea since that gave a new formulae for the energy distribution and resulted in the theory of black-body radiation we have today, one which matches with every experimental observation we have ever done. Whether that's an earth-bound spatial box or the sun.

[Anonymous No.15125399]

>>15125042
*cough cough* I'm gonna need l'Hospital in a
moment, my limits are getting indeterminated

[Anonymous No.15125661]

Are all brown hair genes always dominant?

[Anonymous No.15125943]

>>15125042
I don't care and will continue to use the archaic spelling.

[Anonymous No.15125966]

>>15106588
Bump, anons please help

[Anonymous No.15126094]

>>15124539
That's not even true, Marx was a fan of Darwin but Darwin never wrote back. In general you're right though Hegelian dialectics and later historic materialism predicts physical phenomenon such as evolution.

[Anonymous No.15126261]

What is the 1-D equivalent of what a circle is to a sphere?

[Anonymous No.15126265]

>>15126261
A line

[Anonymous No.15126268]

>>15126265
What is its equivalent of a radius?

[Anonymous No.15126275]

>>15126261
Two points equidistant to a center point.

[Anonymous No.15126276]

>>15126261
See open ball.

[Anonymous No.15126283]

>>15125045
>>15125943
Silly, because it wasn't named after a building.
https://en.wikipedia.org/wiki/Guillaume_de_l%27H%C3%B4pital

[Anonymous No.15126292]

>>15126268
>>15126275

[Anonymous No.15126302]

>>15126283
>Guillaume François Antoine, Marquis de l'Hôpital[1] (French: [ɡijom fʁɑ̃swa ɑ̃twan maʁki də lopital]; sometimes spelled L'Hospital;
Read your links.

[Anonymous No.15126350]

How do I stop myself from being addicted to the taste of ranch on pizza?

[Anonymous No.15126408]

>>15104536
This is the first time I’ve had a full three nights not sleeping since I went on medication in 2017-2018. Is it serious enough to show my condition of schizophrenia is exacerbated or should I just try nap with a nice book and some sleeping aids?

[Anonymous No.15126411]

Suppose we have a real-valued function that we know to be Lipschitz continuous. Can we identify the maximum of the derivative of this function with the Lipschitz constant? I'd say yes, because of the mean value theorem. Since there is at least one point at which the tangent is parallel to the secant. What's your take on this?

[Anonymous No.15126438]

>>15108636
Stat inference by Casella & Berger is great idk what your problem is, fella

[Anonymous No.15126444]

>>15126438
>Doesn't prove half of the theorems he mentions
>great
Let me guess: CS grad?

[Anonymous No.15126449]

>>15126444
bullseye asshole. Friendly reminder that I will earn six figures, while you read your favorite proofs during your 30min lunchbreak at your burgerking job

[Anonymous No.15126453]

>>15126444
Am practicing Biostatistician and I will forever stand by my hero and waifu Jim Berger.

Some proofs are beyond the scope of the intended audience, some aren't worth mentioning idk what you're looking for in a late undergrad early grad text.

>>15126449
lol am not this guy

[Anonymous No.15126457]

>>15126453
>Biostatistician
Combining biology with mathematics is cool.

[Anonymous No.15126525]

>>15126449
lol keep dreaming monkey boy

[Anonymous No.15126527]

>>15126453
>Some proofs are beyond the scope of the intended audience, some aren't worth mentioning
Maybe, but it not discussing characteristic functions is absurd.

[Anonymous No.15126551]

I have a Calculus exam very soon and im wondering if anyone has a cheat sheet with all the basic things that you never really memorize but look up when you need them (like trig identity formulas or i dont know how the inverse of the hyperbolic cosine is defined) because i need to actually memorize them

[Anonymous No.15126607]

>>15126551
Practice deriving them. The sum identities sin(a+b)/cos(a+b) can be derived from R(a)R(b)=R(a+b) where R is the 2x2 rotation matrix [cos(a),-sin(a); sin(a),cos(a)]. Or using e^ix=cos(x)+i.sin(x) and e^a.e^b=e^(a+b). Multiple angle identities are just repeated application of the sum identities (or e^inx=(e^ix)^n). The half-angle identities are the inverse of cos(2h)=cos^2(h)-sin^2(h) = 2cos^2(h)-1 = 1-2sin^2(h). Product-to-sum is just the sum identities in reverse. Hyperbolic functions are cosh(x)=(e^x+e^-x)/2=, sinh(x)=(e^x-e^-x)/2. For their inverses, set e^x=y, e^-x=1/y, solve for y, x=ln(y).

[Anonymous No.15126669]

>>15126283
>>15126302
Not only that, but if you check the note:
> In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. However, French spellings have been altered: the silent 's' has been removed and replaced with the circumflex over the preceding vowel. The former spelling is still used in English where there is no circumflex

[Anonymous No.15126723]

>struggling hard with calc 2
>having to retake it this semester because I got a D last time
Am I stupid? I always thought I was a prodigy at math but I can't seem to grasp most of these concepts

[Anonymous No.15126744]

>>15126411
It's true, when the Lipschitz continuous function is differentiable

[Anonymous No.15126885]

new thread time?

[Anonymous No.15126987]

>>15126885
Just make it lmao, I'm not in a hurry and will probably only do it tomorrow.

[Anonymous No.15127032]

Correct me if I'm wrong, but in a centrifugal space station where gravity is simulated by the spin of the structure would there essentially be no downward "pull" as long as you're not touching the surface of the station? Like, if you're inside and you jump up you wouldn't come down would you?

[Anonymous No.15127041]

your legs would need to be exceptionally strong to nullify what the spin has already done

[Anonymous No.15127104]

I will be handling KOH and NaOH and their solutions in methanol.
What exactly should I wear for protection? Are green rubber gloves+ chemical Google's + some kind of Hazmat suit proper for this kind of hazard?

[Anonymous No.15127216]

>>15127032
> if you're inside and you jump up
Since you are in a rotating frame of reference when you jump up that isn't in a straight trajectory towards the center of rotation. So you will "curve" towards the floor and land in a position some distance ahead of where you started.

[Anonymous No.15127274]

>>15126350
Don't add ranch on pizza. Easy as that.

[Anonymous No.15127796]

>>15127216
Okay. So because I'm already in motion due to the spin I'd still be in motion even if I think I'm jumping straight up, which will lead to me "landing" at another place?

What if I climb a ladder towards the center of the rotation? Would there be any force acting to draw me back down to the surface?

[Anonymous No.15127810]

>>15127796
> which will lead to me "landing" at another place?
Yes. Think of it of having a higher angular velocity compared to the "space" higher up so your position can't remain fixed.

> Would there be any force acting to draw me back down to the surface?
No but there would be a centripetal force at right angles to it, so rather than pulling you down it would pull you to the side.

[Anonymous No.15127969]

Midwit here. How do I survive dynamics? Its my first weeder class and I’m nervous about it.

[Anonymous No.15127976]

>>15127969
read the book

[Anonymous No.15128369]

how should i study for a GED, i haven't gone to school since i was in elementary. just recently turned 19 and realized i'm completely fuarked unless i get one, i'm not very well versed in most subjects but i'm pretty well educated in programming (familiar with x86 asm, cpp, ansi c, js) yet i am still abhorrent at math being unable to do basic geometry. if any anons could suggest some resources that would help me get a decent score that would be very appreciated, i would like to go to college and get a compsci degree so i wish to get an above average score.

[Anonymous No.15128418]

>>15128369
What to read after Aluffi?

[Anonymous No.15128426]

What to read after Aluffi?

[Anonymous No.15128487]

>>15124951
>Correction: it's symmetrical if it can be represented with a symmetrical matrix in an orthogonal basis.
Otherwise diagonalizable would always imply orthogonally diagonalizable.

Right. If anyone cares I was supposed to say that the endomorphism is not orthogonally diagonalizable because the eigenvectors associated to distinct eigenvalues aren't orthogonal one another. And tell me if what I'm about to write is right:
>if the eigenvectors (or some vectors in general) aren't orthogonal one another, then the matrix made by taking those vectors as columns can't be orthogonal, therefore in this case the matrix representing the endomorphism can't be orthogonal

I'm not entirely sure of what I just wrote does it make any sense? And if it doesn't then why do non orthogonal eigenvectors imply a non orthogonally diagonalizable Matrix/endomorphism?

[Anonymous No.15128648]

>>15128369
Start with Terence Tao's Analysis.

[Anonymous No.15128686]

>>15128487
>I'm not entirely sure of what I just wrote does it make any sense?
I'd say it's a very weird way to reason it out.
>And if it doesn't then why do non orthogonal eigenvectors imply a non orthogonally diagonalizable Matrix/endomorphism?
Because orthogonal diagonalizability implies the eigenvectors (of different eigenvalues) are orthogonal. You're looking at not B implies not A, but what you usually prove is A implies B (but apparently you haven't seen the result or forgot about it, hence the confusion).

If [math]A[/math] is symmetric, the vector [math]u[/math] has eigenvalue [math]\lambda_u[/math], [math]v[/math] has [math]\lambda_v[/math], then [math]\lambda_v u^T v = u^T A v = v^T A^T u = v^T A u = \lambda_u v^T u = \lambda_u u^T v[/math], hence either [math]u^T v = 0[/math] or [math]\lambda_u = \lambda_v[/math]

[Anonymous No.15128930]

>>15128686
i see, thanks